Transit of sun through the seasonal nakṣatra cycle in the Vṛddha-Gārgīya Jyotiṣa¶

Indian Journal of History of Science, 56.3(2021)¶

Supplementary Material¶

Fig 1 - Yearly variation of the nakṣatra location error Ey in the seasonal solar zodiac of VGJ.¶

  • The green curves (....83 stars; ___ 27 proxy stars; -.-.-. 9 seasonal nakṣatra) refer to the Ādityacāra data of the 11th Section of VGJ.
  • The 83 constituent and the 27 proxy stars are as per Table 1.
  • Errors for the nine seasonal nakṣatra boundaries remain zero during 1210-1150 BCE.
  • The red curves refer to the twelve month solar nakṣatra data available in the 59th Section titled Ṛtusvabhāva.
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Fig. 2. Error sensitivity for possible identification of Vedic star śraviṣṭhā as β Aquari and śravaṇa as β Delphini.¶

  • The readjusted 27 proxy stars and the yogatāras of Abhyankar lead to almost the same result of c 1250 BCE for the error minimum.
  • Errors for the nine seasonal nakṣatra boundaries remain zero during 1700–1350 BCE.
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Fig.3. Twelve month (madhu-tapasya) or (caitra-phālguna) sun’s transit in 500 BCE as per the Ṛtusvabhāva (59th aṅga) of VGJ.¶

  • The points are joined smoothly for better visualization with markings for the seasons and the months.
  • It can be verified that all the twelve nakṣatra named in the VGJ text would have been visible sometime in the specified months.
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One Year full moon overlaid on Seasons and Nakṣatras for -1500¶

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One Year full moon overlaid on Seasons and Nakṣatras for -1500¶

  • Plot of RA and Dec and Full Moon size indicated
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One Month moon overlaid on Seasons and Nakṣatras for -1500¶

  • Plot of RA and Dec ; Black is krishna paksha, Blue is shukla paksha
  • Size indicates the phase of the moon
<Axes: title={'center': 'Moon Path - two nakshatra cycles - at -500\n Blue is shukla paksha and black krishna'}>
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Plot of Nakṣatra locations in their respective divisions¶

  • Red Band indicates where the nakṣatra bound is highest
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Seasons per Ādityacāra¶

  श्रविष्ठादीनि चत्वारि पौष्णार्धञ्च दिवाकरः । वर्धयन् सरसस्तिक्तं मासौ तपति शैशिरे ॥   
  रोहिण्यन्तानि विचरन् पौष्णार्धाद्याच्च भानुमान् । मासौ तपति वासन्तौ कषायं वर्धयन् रसम् ॥          
  सार्पार्धान्तानि विचरन् सौम्याद्यानि तु भानुमान् । ग्रैष्मिकौ तपते मासौ कटुकं वर्धयन् रसम् ॥   
  सावित्रान्तानि विचरन् सार्पार्धाद्यानि भास्करः । वार्षिकौ तपते मासौ रसमम्लं विवर्धयन् ॥    
  चित्रादीन्यथ चत्वारि ज्येष्ठार्धञ्च दिवाकरः । शारदौ लवणाख्यं च तपत्याप्याययन् रसम् ॥                   
  ज्येष्ठार्धादीनि चत्वारि वैष्णवान्तानि भास्करः । हेमन्ते तपते मासौ मधुरं वर्धयन् रसम् ॥ 
  (Ādityacāra; v. 47, 48, 52, 53, 54, 55)
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Table 1. Nakṣatra Constituents and proxy stars of the 11th Section of VGJ.¶

nid nakshatra rep_star vis_start_epoch vis_end_epoch left_bound right_bound num_stars_in_naks stars_in_naks daivata
#
1 (N01-Ash,) Aśvayuk β Ari -2100 -1200 350.00 336.67 3 α Ari;β Ari;γ Ari Aśvini
2 (N02-Bha,) Bharaṇī * 41 Ari -2200 -1250 3.33 350.00 3 * 35 Ari;* 39 Ari;* 41 Ari Yama
3 (N03-Kri,) Kṛttikā η Tau -2050 -1150 16.67 3.33 6 * 17 Tau;* 19 Tau;* 20 Tau;* 23 Tau;* 27 Tau;η... Agni
4 (N04-Roh,) Rohiṇī α Tau -1800 -900 30.00 16.67 5 α Tau;γ Tau;δ Tau;ε Tau;θ2 Tau Prajāpati
5 (N05-Mrg,) Mṛgaśira λ Ori -1850 -950 43.33 30.00 3 α Ori;γ Ori;λ Ori Soma
6 (N06-Ard,) Ārdrā γ Gem -2000 -1100 56.67 43.33 1 γ Gem Rudra
7 (N07-Pun,) Punarvasu β Gem -2100 -1200 70.00 56.67 2 α Gem;β Gem Aditi
8 (N08-Pus,) Puṣya δ Cnc -2200 -1300 83.33 70.00 1 δ Cnc Bṛhaspati
9 (N09-Asl,) Āśleṣā ζ Hya -1700 -750 96.67 83.33 6 δ Hya;ε Hya;ζ Hya;η Hya;ρ Hya;σ Hya Sarpa
10 (N10-Mag,) Maghā ζ Leo -1650 -750 110.00 96.67 6 α Leo;γ Leo;ε Leo;ζ Leo;η Leo;μ Leo Pitṛ
11 (N11-PPal,) P Phalgunī δ Leo -1650 -750 123.33 110.00 2 δ Leo;θ Leo Bhaga
12 (N12-UPal,) U Phalgunī β Leo -1500 -550 136.67 123.33 2 * 93 Leo;β Leo Aryaman
13 (N13-Has,) Hasta δ Crv -2100 -1150 150.00 136.67 5 α Crv;β Crv;γ Crv;δ Crv;ε Crv Savitṛ
14 (N14-Chi,) Citrā α Vir -1850 -950 163.33 150.00 1 α Vir Tvaṣṭṛ
15 (N15-Swa,) Svātī α Boo -900 0 176.67 163.33 1 α Boo Vāyu
16 (N16-Vis,) Viśākhā α2 Lib -1450 -550 190.00 176.67 2 α1 Lib;α2 Lib Indrāgnī
17 (N17-Anu,) Anūrādhā δ Sco -1750 -850 203.33 190.00 4 β1 Sco;δ Sco;π Sco;ω1 Sco Mitra
18 (N18-Jye,) Jyeṣṭhā ε Sco -1750 -850 216.67 203.33 3 α Sco;ε Sco;σ Sco Indra
19 (N19-Mul,) Mūla κ Sco -1550 -650 230.00 216.67 6 ζ2 Sco;θ Sco;ι1 Sco;κ Sco;λ Sco;ν Sco Nirṛti
20 (N20-PAsh,) P Aṣāḍhā λ Sgr -1300 -400 243.33 230.00 4 γ Sgr;δ Sgr;ε Sgr;λ Sgr Ap
21 (N21-UAsh,) U Aṣāḍhā τ Sgr -950 -50 256.67 243.33 4 ζ Sgr;σ Sgr;τ Sgr;φ Sgr Viśvedevā
22 (N22-Shr,) Śravaṇa α Aql -1200 -300 270.00 256.67 3 α Aql;β Aql;γ Aql Viṣṇu
23 (N23-Dha,) Dhaniṣṭhā β Del -1300 -400 283.33 270.00 4 α Del;β Del;γ2 Del;δ Del Vasu
24 (N24-Sha,) Śatabhiṣak λ Aqr -2200 -1250 296.67 283.33 1 λ Aqr Varuṇa
25 (N25-PBha,) P Proṣṭapada α Peg -2100 -1150 310.00 296.67 2 α Peg;β Peg Aja
26 (N26-UBha,) U Proṣṭapada α And -1100 -150 323.33 310.00 2 α And;γ Peg Ahirbudhnya
27 (N27-Rev,) Revatī ε Psc -1900 -950 336.67 323.33 1 ε Psc Pūṣan

Path of Mars without and with Vakra¶

This chart that shows

  • Mars path from Jyeshta(1) to Jyeshta(2) to Jyestha(3) .
  • Epoch is around -590
  • Mars takes ~540 days from Jyeshta(1) to Jyeshta(2) ( no Vakra)
  • Mars takes ~720 days from Jyeshta(2) to Jyeshta(3) ( Vakra)
  • The mars path is color coded - blue visible, red not visible
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Plot of Sun-Gruha angular gap annotated with visibility and rise/set events¶

Writing to file ../datasets/mercury-events.tsv
Writing to file ../datasets/venus-events.tsv
Writing to file ../datasets/mars-events.tsv
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Venus morning/evening first/last visibility¶

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